Labour MP Tom Watson has accused Conservative select committee colleague Louise Mensch of tabling amendments that would have "exonerated" James Murdoch in its controversial phone hacking report following a personal intervention by the son of media tycoon Rupert Murdoch.

The row over the Commons culture, media and sport select committee's phone-hacking report pronouncing Rupert Murdoch unfit to run an international company escalated further on Thursday, with Watson saying that had the Tories on the committee had their way the would have issued a whitewash report that was "inspid to the point of being craven".

Watson also hit out against the two other Conservative MPs on the committee, Therese Coffey and Philip Davies, and called on chairman John Whittingdale to publish earlier drafts of the controversial report to back up his claim that the Tories had tried to water it down.

"When James Murdoch sent an unsolicited second letter to the committee it was used by Louise Mensch to table a number of amendments effectively exonerating Murdoch junior from any of the accusations made by Colin Myler and Tom Crone," Watson said, in reference to the News of the World's former editor and head of legal.

"Our deliberations were further hampered by Dr Therese Coffey, who persistently stated she would draw conclusions based only on the evidence submitted to the committee – explicitly ruling out all evidence from the public domain, including testimony at the Leveson inquiry and all the civil cases [brought by phone hacking victims].

"To complete the trinity, we had Philip Davies – a man who bitterly complained that [Labour MP] Paul Farrelly and I were partisan when the committee published its previous report in 2009. He was so independent minded then he wrote a column in the News of the World to make his claims."

Mensch hit back at Watson's suggestion that she had somehow caved into pressure from News International. "Tom is free to publish all the amendments. There is nothing secret about it," she said.

She added that she had one briefing from News Corp's European public affairs director, Frédéric Michel, earlier this year, but she told him in advance she could not discuss the deliberations of the select committee.

"He gave me a briefing on the [News Corp] management and standards committee, information on the arrests at the Sun. This was all after the arrests at the Sun. I took that briefing and I declared it to the committee the next day. I was offered a briefing over the summer, but declined," Mensch said.

"To carry on suggesting that undue pressure was applied and I caved in is just wrong. I found Mr Murdoch's evidence convincing and I speak as I find," she added.

Mensch tabled, she believes, "half a dozen amendments", not all of them which would have got through to a vote. But the three main amendments, which the Guardian has seen, included requests to include large chunks of Murdoch's letter in the final report.

The most significant of the three relates to paragraph 162 of the report which states the committee is "astonished that James Murdoch did not seek more information" in relation to the £700,000 phone-hacking settlement in 2008 with Gordon Taylor, the chief executive of the Professional Footballers Association.

Mensch and Coffey did not pass judgment on Murdoch for being so incurious and wanted to amend the paragraph to an observation that "it would have been better had he not relied on Mr Crone and Mr Myler's account, and requested to see more documentation".

A second amendment again related to inserting a portion of Murdoch's letter and a third was a request to change the word "astonishing" to "surprising" in relation to another finding.

Watson described Mensch's amendments as "lick spittle". But Mensch hit back saying she saw no reason not to include chunks of Murdoch's letter in the report and said she found him to be a "compelling" and "consistent witness".

"There is nothing secret or underhand about it. I found he was a compelling witness and I thought we should record what he said. I thought it was only fair," she added.

Amendments put forward by Coffey also sought to tone down the criticism of Murdoch. She suggested replacing "however keen senior executives may have been to delegate" with "we recognise that delegation is normal in any company".

She also wanted a reference to "such executive carelessness" replaced with "this lack of judgment".

Coffey requested the word "shield" be changed to "obscure" in a sentence in paragraph 207, which asks if the lack of openness of senior management can be explained by "a deliberate policy of 'don't ask, don't tell' designed to 'shield' senior executives from events taken beneath them". She also objected to the "don't ask, don't tell" phrase and wanted to replace it "don't tell the family".

In the letter, Murdoch once again protested his innocence and denied he had misled parliament. He maintained that Crone and Myler could have disclosed more in 2008 if they had "wanted to warn me that voicemail interception was more widespread". Instead, he said: "They said nothing that led me to believe a further investigation was necessary."

This was a position ultimately taken up by the select committee. Its report, published on Tuesday, accused Myler and Crone of misleading parliament but cleared Murdoch, instead criticising him for "wilful ignorance" about the extent of phone hacking at the News of the World.

Watson claimed the original draft of the report by Whittingdale, the Conservative MP and culture select committee chairman, was "was insipid to the point of being craven towards News International".

"Without the steady hand of an experienced journalist, Paul Farrelly, who painstakingly and patiently moved dozens of amendments – so powerful in their logic they were accepted unanimously – and the wise counsel of Adrian Sanders – who came under enormous pressure – we would have ended up with a whitewash," he said.

Watson made his comments on Thursday after a Twitter spat earlier in the day with Mensch over the decision by the four Tories on the select committee to vote against amendment 229 declaring Murdoch "not a fit person to exercise the stewardship of a major international company".

In an hour of testy back and forth, prompted by Mensch's appearance on Today, Watson threatened to publish all the amendments Tory MPs on the committee had put forward for the report.

When Mensch replied that he ought to make sure he included a timeline of the amendments, Watson tweeted: "You mean James Murdoch's second letter that seemed to uncannily answer concerns raised in private discussions? No problem."

Mensch hit back: "Are you accusing me of something? Not like you. Don't let temper get better of you. 'Fit' was error."

Watson told the Guardian: "Now that Louise has felt the need to breach the convention that our private deliberations remain that way, we might as well have it out."

He said the best solution was to have the draft report published, which would show a timeline of all amendments proposed by Conservative and Labour committee members as the report was drafted and redrafted over three months.

"In helping the public form a judgment, I would support the chairman of the committee were he to publish the original draft of the report and all amendments tabled by all members of the committee," Watson said.

"People will make up their own mind as to the integrity and motives of the committee members. It might also help the public debate were all committee members to publish their meetings with employees of News International and BSkyB as well as all hospitality and social invitations."

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